RADIATIVE EQUILIBRIUM 
105 
Multiply (74-1) first by dco/477- and integrate, and secondly by dco cos 0/4-77 
and integrate. We obtain 
The second equation agrees with (7IT) except that the actual operative 
stress-component p R ' appears instead of the hydrostatic approximation 
Pr• Reference to (74-2) shows that the error caused by using p R does not 
depend on the fore-and-aft asymmetry arising from the presence of a net 
In strict thermodynamical equilibrium with no outward flow H this 
becomes 
giving the well-known law that the emission coefficient is proportional to 
the absorption coefficient for different kinds of matter at the same tempera 
ture. 
75. Let E (0) be expanded in zonal harmonics, viz. 
E (6) — A + BP 1 (cos 9) + CP 2 (cos 9) + DP Z (cos 9) + ... (75T). 
By integration over a sphere, 
Hence the first three coefficients in the expansion have the interpretation 
(74-3), 
dp R _ kpH 
(74-4). 
dr c 
flow H, but on the much smaller radial-transverse asymmetry which 
makes the weighted mean value of cos 2 9 differ slightly from 
Equation (74*3) can be written 
or 
cE = j/k, 
j -= kacT 4 
(74-5) 
Multiplying the series by cos 9 and integrating, 
H/c = ~ j E {9) P 1 (cos 9) doj = [ {P 1 (cos 0)} 2 do> = 
Multiplying by P 2 (cos 9) = f cos 2 0 — and integrating, 
I ( Pr ~ Pr) = f {f E (9) cos 2 9 - (9)} dco 
{P 2 (cos 9)Y dco 
A = E, B = 3 H/c, C = (pr' - pr) (75-2).